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Solving complex linear equations

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Lesson details

Learning outcome

I can solve complex linear equations, including those involving reciprocals.

Key learning points

  1. Any linear equation written in the form Ax + B = C can be solved.
  2. Equations involving division by a constant can be manipulated to reach the form Ax + B = C.
  3. Equations involving division by a variable can be manipulated to reach the form Ax + B = C.

Keywords

  • Equation - An equation is used to show two expressions that are equal to each other.

Common misconception

Pupils often "multiply through by $$5$$" and turn $${{2x+1}\over5}={10}$$ into $${{10x+5}}={50}$$

Use equivalent fractions as opposed to multiplying through. In one simple step $${{2x+1}\over5}={10}$$ becomes $${{2x+1}\over5}={50\over5}$$

Teacher tip

The key is for pupils to be able to fluently use their fractions skills and knowledge when manipulating algebra. Use a numerical fractions starter to ensure they recall key skills like multiplying a fraction by an integer, and by another fraction.

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
 except where otherwise stated. See Oak's terms & conditions
 (Collection 2).

Lesson video

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Prior knowledge starter quiz

Download starter quiz questions (PDF)

6 Questions

Q1.
$$1\over7$$ is the of $$7$$

fraction
division
Correct answer: reciprocal
divisor
multiplier

Q2.
Solve $$6x+9=27$$

Correct answer: $$x=3$$
$$x=6$$
$$x=9$$
$$x=18$$

Q3.
Solve $${x\over3}=15$$

Correct answer: $$x=45$$
$$x=18$$
$$x=5$$
$$x={1\over5}$$

Q4.
Calculate $${2\over3}\times{4\over5}$$

$$6\over15$$
$$6\over20$$
Correct answer: $$8\over15$$
$$10\over12$$
$$12\over10$$

Q5.
Which of these expressions are equivalent to $${{x+1}\over3}\times{2\over3}$$ ?

$${2x+1}\over9$$
Correct answer: $${2{(x+1)}\over9}$$
$${2{(x+1)}\over3}$$
$${2x+2}\over3$$
Correct answer: $${2x+2}\over9$$

Q6.
Expand and simplify $$8({{x}\over8})$$

$$8$$
Correct answer: $$x$$
$$8x$$
$${{8x}\over8}$$
$$x=8$$

Assessment exit quiz

Download exit quiz questions (PDF)

6 Questions

Q1.
$${{56}\over{y}}=7$$ is an example of a equation.

variable
Correct answer: rational
irrational
special

Q2.
The solution to $${{6x−2}\over{4}}=7$$ is $$x=$$

Correct Answer: 5, five

Q3.
Solve $${{2x}\over{3}}+1=11$$

Correct answer: $$x=15$$
$$x=16$$
$$x=17$$
$$x=18$$

Q4.
Which is the most efficient first step when solving the equation $${{x+7}\over{9}}={{x-1}\over{3}}$$ ?

Subtract $$7$$ from both sides.
Add $$1$$ to both sides.
Correct answer: Multiply both sides by $$9$$
Multiply both sides by $$3$$
Multiply both sides by $$27$$

Q5.
Solve $${{x+7}\over{9}}={{x−1}\over{3}}$$. The solution is $$x=$$

Correct Answer: 5, five

Q6.
Solve $${{32}\over{3x}}=8$$

$$x={3\over4}$$
$$x=3$$
$$x=4$$
Correct answer: $$x={4\over3}$$

To help you plan your 8 maths lesson on: Solving complex linear equations, download all teaching resources for free and adapt to suit your pupils' needs...